5/4/2017

MORPH 2017

AARHUS UNIVERSITY

4-5 May

Moesgaard Campus

A Conference on the Archaeological Applications of Morphometrics

Credits

  • Laboratory of Forensic Anthropology, University of Coimbra

  • Paleoecology and Forensic Sciences Group of CFE, University of Coimbra

Introduction

  • Non-metric (or morphological) vs. metric
  • Rogers (1999) introduces new method for sex estimation
    • non-metric, using only the distal humerus
    • 4 traits:
      • Olecranon fossa shape
      • Angle of the medial epicondyle
      • Throclear Extension / Symmetry
      • Throclear Constriction
    • 74-94% overall accuracy
    • seems to be somewhat reliable in juveniles (~81% accuracy in Rogers, 2009)
  • Falys et al (2005) tested the method
    • 69-82% accuracy
  • Vance et al (2011) also tested it
    • 74-79% accuracy

Trait description

Rogers (1999); Falys et al (2005).

Trait description

Rogers (1999); Falys et al (2005).

Trait description

Rogers (2009)

Trait description

Vance et al. 2011

Trait description

Rogers (1999); Falys et al (2005).

Materials, Methods

  • 80 female and 71 male humeri (left side)
  • from the 21st Century Identified Skeletal Collection (CEI/XXI)
    • at the University of Coimbra, Portugal.
  • All specimens were photographed in standardized position
    • from the posterior view
    • by placing the subject on a flat table
    • and the camera directly above the olecranon fossa.
  • With TPSdig2 (Rohlf, 2006) we digitized
    • open curves
    • closed outlines

The first evaluated the constriction of the trochlea, with the curve reaching from the most medial inferior aspect to the most lateral inferior aspect of the trochlea. The second described the outline of the olecranon fossa and was recorded clockwise starting from its most inferior aspect.

What did we look at?

Individual 4 (female) and Individual 6 (male) of the CEI/XXI collection.

Materials, Methods 2

  • All the analyses were performed using the R programming language (R Core Team 2017)
    • and the Momocs package developed by Bonhomme et al. (2014).
  • Generalized Procrustes analysis (GPA) as first proposed by Gower (1975).
  • Natural 8 degrees polynomials fits were used to define the open curve of the trochlea
  • An elliptical Fourier transform was used for the closed outline of the olecranon fossa
    • 99% of the harmonic power was kept
    • in this case, that represented 6 harmonics

From then on, both sets of data were processed with the same statistical algorithms.

Materials, Methods 3

Hereby, both sets of data were processed with the same statistical algorithms.

  • Principal component analysis (PCA) to reduce dimensionality, and to visualize the morphospace.
  • Linear discriminant analyses (LDA)
    • using the principal components, to estimate the sex from shape configurations
    • trained on a K = n - 1 cross-validation scheme to avoid overfitting
  • The method was implemented into a webapp, through the Shiny package (Chang et al, 2017)

This follows the recent trend in forensic anthropology, which attempts to make complicated statistical models more accessible and easier to utilize through interactive online applications (e.g. Navega et al., 2015; Gonçalves et al, 2016; Curate et al, 2016).

Throclear Constriction - Exploratory Analysis 1

Throclear Constriction - Exploratory Analysis 2

Throclear Constriction - Polynomial Fit + PCA

TC.n <- npoly(TC.aligned, nb.pts = 16, degree = 8)
TC.pca <- PCA(TC.n)
TC.pca %>% plot(., "Sex", col = palet)

Throclear Constriction - PCA morphospace

TC.pca %>% as_df() %>% ggplot() + aes(x = PC1, y = PC2, col = Sex) +
    geom_point() + geom_density2d() + theme_light()

Throclear Constriction - Mean shapes

TC.ms <- mshapes(TC.n, 1)
TC_female <- TC.ms$shp$Female %T>% coo_plot(border = palet[1])
TC_male <- TC.ms$shp$Male %T>% coo_draw(border = palet[2])
legend("topright", lwd = 1, col = palet, legend = c("Female", "Male"), cex = 0.8)

Throclear Constriction - Shape deformation 1

tps_grid(TC_female, TC_male, shp.border = palet)

Throclear Constriction - Shape deformation 2

tps_arr(TC_female, TC_male, shp.border = palet)

Throclear Constriction - Shape deformation 3

tps_iso(TC_female, TC_male, shp.border = palet)

Throclear Constriction - Inferential Statistics

MANOVA(TC.pca, 1)
## PC axes 1 to 2 were retained
##            Df Hotelling-Lawley approx F num Df den Df  Pr(>F)  
## fac         1         0.031687   2.3448      2    148 0.09942 .
## Residuals 149                                                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Throclear Constriction - LDA 1

TC.lda <- LDA(TC.pca, 1)
## 0.99 total variance
## 2 PC retained
TC.lda
##  * Leave-one-out cross-validation ($CV.correct): (60.9% - 92/151): 
## 
##  * Class correctness ($CV.ce):
##    Female      Male 
## 0.7875000 0.4084507 
## 
##  * Cross-validation table ($CV.tab):
##         classified
## actual   Female Male
##   Female     63   17
##   Male       42   29

Throclear Constriction - LDA 2

plot(TC.lda, palette = cores2)

## NULL

Olecranon Fossa - Exploratory Analysis 1

Olecranon Fossa - Exploratory Analysis 2

Olecranon Fossa - Elliptical Fourier + PCA

OF.ef <- efourier(OF.aligned, nb.h = 6)
OF.pca <- PCA(OF.ef)
OF.pca %>% plot(., "Sex", col = palet)

Olecranon Fossa - PCA morphospace

OF.pca %>% as_df() %>% ggplot() + aes(x = PC1, y = PC2, col = Sex) + coord_equal() + 
    geom_point() + geom_density2d() + theme_light()

Olecranon Fossa - Mean shapes

OF.ms <- mshapes(OF.ef, 1)
OF_female <- OF.ms$shp$Female %T>% coo_plot(border = palet[1])
OF_male <- OF.ms$shp$Male %T>% coo_draw(border = palet[2])
legend("topright", lwd = 1, col = palet, legend = c("Female", "Male"), cex = 0.8)

Olecranon Fossa - Shape deformation 1

tps_grid(OF_female, OF_male, shp.border = palet)

Olecranon Fossa - Shape deformation 2

tps_arr(OF_female, OF_male, shp.border = palet)

Olecranon Fossa - Shape deformation 3

tps_iso(OF_female, OF_male, grid = TRUE, shp.border = palet)

Olecranon Fossa - Inferential Statistics

MANOVA(OF.pca, 1)
## PC axes 1 to 7 were retained
##            Df Hotelling-Lawley approx F num Df den Df    Pr(>F)    
## fac         1           1.8666   38.133      7    143 < 2.2e-16 ***
## Residuals 149                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Olecranon Fossa - LDA 1

OF.lda <- LDA(OF.pca, 1)
## 0.99 total variance
## 7 PC retained
OF.lda
##  * Leave-one-out cross-validation ($CV.correct): (92.1% - 139/151): 
## 
##  * Class correctness ($CV.ce):
##    Female      Male 
## 0.9500000 0.8873239 
## 
##  * Cross-validation table ($CV.tab):
##         classified
## actual   Female Male
##   Female     76    4
##   Male        8   63

Olecranon Fossa - LDA 2

plot(OF.lda, palette = cores2)

## NULL

Olecranon Fossa - Can we make a better model?

By better we mean:

  • as simple as possible
  • keeping similar levels of overall accuracy
  • applicable!!!
cor(OF.pca$x[,1:7], as.numeric(OF.pca$fac$Sex)) # correlations
##            [,1]
## PC1  0.05302026
## PC2  0.46336920
## PC3 -0.11872418
## PC4  0.63185511
## PC5 -0.09388462
## PC6  0.05482801
## PC7  0.09208552

Let's see if it makes sense. Little exclusive for Morph2017

Olecranon Fossa - PCA morphospace

OF.pca %>% as_df() %>% ggplot() + aes(x = PC2, y = PC4, col = Sex) + 
    geom_point() + geom_density2d() + theme_light()

Olecranon Fossa - A simpler model

OF.lda2 <- LDA(OF.pca$x[,c(2,4)], OF.pca$fac$Sex)
OF.lda2
##  * Leave-one-out cross-validation ($CV.correct): (91.4% - 138/151): 
## 
##  * Class correctness ($CV.ce):
##    Female      Male 
## 0.9375000 0.8873239 
## 
##  * Cross-validation table ($CV.tab):
##         classified
## actual   Female Male
##   Female     75    5
##   Male        8   63

This has been implemented in an interactive, easy-to-use, free to all, way:

Credits

  • Laboratory of Forensic Anthropology, University of Coimbra

  • Paleoecology and Forensic Sciences Group of CFE, University of Coimbra